Size preserving mesh generation in adaptivity processes

It is well known that the variations of the element size have to be controlled in order to generate a high-quality mesh. Hence, several techniques have been developed to limit the gradient of the element size. Although these methods allow generating high-quality meshes, the obtained discretizations do not always reproduce the prescribed size function. Specifically, small elements may not be generated in a region where small element size is prescribed. This is critical for many practical simulations, where small elements are needed to reduce the error of the numerical simulation. To solve this issue, we present the novel size-preserving technique to control the mesh size function prescribed at the vertices of a background mesh. The result is a new size function that ensures a high-quality mesh with all the elements smaller or equal to the prescribed element size. That is, we ensure that the new mesh handles at least one element of the correct size at each local minima of the size function. In addition, the gradient of the size function is limited to obtain a high-quality mesh. Two direct applications are presented. First, we show that we can reduce the number of iterations to converge an adaptive process, since we do not need additional iterations to generate a valid mesh. Second, the size-preserving approach allows to generate quadri- lateral meshes that correctly preserves the prescribed element size.Peer ReviewedPostprint (published version

Seven Cases Unstructured Triangulation Technique for Simplified Version of Conceptual Model of Ethylene Furnace for Radiative Heat Transfer Approximation

In this paper, we introduce a new enhanced method utilizing the approach of advancing front technique for generating unstructured meshes in the simplified version of ethylene conceptual model. The method is called as Seven Cases Unstructured Triangulation Technique (7CUTT) where it is based on seven categories of cases for element creation procedure and the layer concept for mesh gradation control. The algorithm of the mesh incorporates sensor deployment in its conceptual model to supply input for boundary values. The quality of the mesh is determined based on a measurement in GAMBIT software. 7CUTT provides the framework for the heat to be approximated using the discrete ordinate method, which is a variant of the finite volume method. Simulation results produced using FLUENT support the findings for effectively approximating the flue gas temperature distribution in the simplified furnace at the end of the study

Tree Structures for Adaptive Control Space in 3D Meshing

The article presents a comparison of several octree- and kd-tree-based structuresused for the construction of control space in the process of anisotropicmesh generation and adaptation. The adaptive control space utilized by theauthors supervises the construction of meshes by providing the required metricinformation regarding the desired shape and size of elements of the mesh ateach point of the modeled domain. Comparative tests of these auxiliary structureswere carried out based on different versions of the tree structures withrespect to computational and memory complexity as well as the quality of thegenerated mesh. Analysis of the results shows that kd-trees (not present inthe meshing literature in this role) offer good performance and may becomea reasonable alternative to octree structures

An insight into the science of unstructured meshes in computer numerical simulation

Computer numerical simulation is a beneficial tool for studying various domains of knowledge. Among the steps in the whole process of numerical simulation is the generation of unstructured meshes. Since the unstructured meshes are usually generated using automatic software, the fundamental knowledge of the unstructured meshes is often neglected. This paper highlighted some useful insights into the unstructured meshes in numerical simulation for several application domains, such as the radiative heat transfer problem, ocean modelling and biomedical engineering. It also reviewed some fundamental concepts and frameworks for element generation in producing unstructured meshes, particularly the Delaunay triangulation and advancing front techniques

Advanced Unstructured Grid Generation for Complex Aerodynamic Applications

A new approach for distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods

Automatic sizing functions for unstructured surface mesh generation

Accurate sizing functions are crucial for efficient generation of high-quality meshes, but to define the sizing function is often the bottleneck in complicated mesh generation tasks because of the tedious user interaction involved. We present a novel algorithm to automatically create high-quality sizing functions for surface mesh generation. First, the tessellation of a Computer Aided Design (CAD) model is taken as the background mesh, in which an initial sizing function is defined by considering geometrical factors and user-specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions and containing a significantly reduced element number. Finally, this sizing function is applied in an advancing front mesher. With the aid of a walk-through algorithm, an efficient sizing-value query scheme is developed. Meshing experiments of some very complicated geometry models are presented to demonstrate that the proposed sizing-function approach enables accurate and fully automatic surface mesh generation

DEFINITION AND INTERPOLATION OF DISCRETE METRIC FOR MESH GENERATION ON 3D SURFACES

The article concerns the problem of a definition of the control space from a set of discretedata (metric description gathered from different sources) and its influence on the efficiency ofthe generation process with respect to 2D and 3D surface meshes. Several methods of metricinterpolation between these discrete points are inspected, including an automated selectionof proper method. Some aspects of the procedures of creation and employment of the meshcontrol space based on the discrete set of points are presented. The results of using differentvariations of these methods are also included

Preparation of Control Space for Remeshing of Polygonal Surfaces

The subject of the article concerns the issues of remeshing, transforming a polygonal mesh into a triangular mesh adapted to surface. From the initial polygonal mesh the curvature of surface and boundary is retrieved and used to calculate a metric tensor varying in three-dimensional space. In the proposed approach the curvature is computed using local approximation of surfaces and curves on the basis of vertices of the polygonal mesh. An essential part of the presented remeshing procedure is creation of a control space structure based on the retrieved discrete data. The subsequent process of remeshing is then supervised by the contents of this auxiliary structure. The article presents various aspects related to the procedure of initialization, creation and adjusting the control space structure

THE SEVEN CASES UNSTRUCTURED TRIANGULATION TECHNIQUE FOR RADIATIVE HEAT TRANSFER APPROXIMATION IN AN ETHYLENE FURNACE CRACKER

Radiative heat distribution inside an ethylene cracker furnace is often modelled using the finite volume and finite element methods. In both cases, meshes in the form of rectangles and triangles are needed to serve as the approximating points in the domain. In this paper, a new method called the Seven Cases Unstructured Triangulation Technique (7CUTT) is proposed for meshing the domain inside the cracker furnace, integrated with the deployment of sensors on the wall to obtain the boundary value. 7CUTT is an enhanced version of the Standard Advancing Front Technique (SAFT) which two normal cases in SAFT are extended to the total of seven cases for consideration during the element creation procedure for initial mesh generation. The focus of this method is to construct the initial triangular meshes with the requirement of (1) having the location of sensors deployed along the wall as boundary nodes as well as forming boundary elements, (2) generating nodes at a certain boundary with linearly different lengths of boundary edges as interior gradation controls and (3) constructing the triangular element directly in every iteration without having to re-order the Front or delete the existing elements. There are three contributions from this paper, the first one is the introduction of seven extended cases for consideration for the element creation procedure, the second is the layer concept to generate edges with linearly different lengths and the third is the post-processing mesh procedure to improve the quality of the mesh that is suitable for 7CUTT. The final mesh is obtained once the post-processing procedure of improving the mesh quality is applied to the initial mesh. 7CUTT provides the framework for the heat to be approximated using the discrete ordinate method, which is a variant of the finite volume method. Simulation results produced using FLUENT support the findings for effectively approximating the flue gas temperature distribution, the circumferential radiative heat flux incident at the reactor coils as well as the circumferential reactor coil temperature in the furnace at the end of the study